Multi-port devices are characterized by their number of ports, typically referred to throughout this application as N, where N is 2 or greater. S-parameter measurement instruments, such as a vector network analyzer (VNA), are used to characterize such a multi-port (i.e., N-port) device under test (DUT, often simply referred to as a “device”) by measuring complex transmission and reflection characteristics of the DUT.
In the RF and microwave regions virtually all devices are characterized by their S (or scattering) matrices. The S matrix is composed of S-parameters. S-parameter measurement is the standard method for device characterization over a very wide range of frequencies, from less than 1 MHz to above 40 GHz. These parameters are used because they are easily determined, they provide directly relevant measures of device performance, and they are well defined for various types of devices. If other device representations are required, such as impedance or admittance parameters, then these can be readily deduced from the measured S-parameters.
More specifically, S-parameters of a multi-port device characterize how the device interacts with signals presented to the various ports of the device. An exemplary S-parameter is “S12”(often shown as “S12”). The first number is the port that the signal is leaving, while the second is the port that the signal is being injected into. S12, therefore, is the signal leaving port 1 relative to the signal being injected into port 2. The four S-parameters associated with an exemplary two-port device are:                S11 is referred to as the “forward reflection” coefficient, which is the signal leaving port 1 relative to the signal being injected into port 1;        S21 is referred to as the “forward transmission” coefficient, which is the signal leaving port 2 relative to the signal being injected into port 1;        S22 is referred to as the “reverse reflection” coefficient, which is the signal leaving port 2 relative to the signal being injected into port 2; and        S12 is referred to as the “reverse transmission” coefficient, which is the signal leaving port 1 relative to the signal being injected into port 2.        
A large number of commercial test systems are available for S-parameter measurement. Such systems are generally referred to as network analyzers. These instruments typically fall into two classes: scalar and vector. Scalar analyzers determine the amplitudes of the S-parameters only, whereas vector analyzers (VNAs) determine both the amplitudes and the phases. Scalar analyzers are far less flexible and far less accurate than vector analyzers, and are typically only employed in low-grade applications where equipment cost is a driving factor. Although embodiments of the present invention are generally applicable to VNA test instruments, the embodiments may also apply to other types of instruments that characterize S-parameters (or other equivalent measurements) for a multi-port DUT.
Commercial VNA systems typically include a signal generator and a combination of splitters and directional couplers that connect the measurement ports of the VNA to its amplitude and phase detection circuitry (samplers). A typical DUT to be characterized by such a VNA has one, two or more ports, typically with coaxial or waveguide interfaces. For an N-port DUT, the S matrix (N×N) can be defined by: b=Sa, where a is an N-component vector containing the amplitudes of the waves incident on the device ports, and b is a vector containing the amplitudes of the outgoing waves. More formally, the wave amplitudes are defined by: ai=(Vi+ZiIi)/2; and bi=(Vi−ZiIi)/2, where ai is the incident voltage wave amplitude, bi is the outgoing voltage wave amplitude, Vi is the voltage, Ii is the input current, and Zi is the normalizing impedance, all for the ith port under test.
The port-normalizing impedances (Zi) are typically chosen to be equal to the characteristic impedances of the coaxial cables in the test system, which are 50 Ω in most cases. If a given port is terminated with its normalizing impedance (a matched load) then the incident wave amplitude at that port is identically zero (from ai=(Vi+ZiIi)/2).
When a DUT is connected to the test ports of a network analyzer, a signal is applied to each device port in succession, and the reflected and transmitted waves are detected with the aid of the directional couplers. The S-parameters for the DUT are then deduced by measuring the amplitude and phase of each of these waves relative to those of the input signal.
In practice, there are inevitable hardware imperfections or errors in any VNA test system, which are principally related to port mismatch, coupler directivity, and instrument frequency response. Without correction, these imperfections can produce significant measurement errors. Such imperfections are typically compensated for though appropriate VNA calibrations. VNA calibrations are typically performed by connecting physical standards (also known as mechanical primary standards) to each of the ports of the VNA for the purpose of calibration. Electrical characteristics of the standards are derived from known physical properties of the standards, such as physical dimension, conductor material, and the like. The errors of the VNA are typically determined by computing the difference between the VNA measured response of the standards and known electrical characteristics of the standards. After the VNA is calibrated, an uncharacterized DUT can be connected to the VNA for measurement, and the errors associated with the VNA (determined during calibration) can then be mathematically removed from the measurement of the DUT. Many modern VNAs include internal automatic calibrators that perform the calibration.
When the number of port of a DUT (N ports) is greater than the number of ports of the VNA (M ports), N-port calibrations are typically performed using multiport test sets, with multiple M-port calibrations overlaid. The other N-M port contributions are either ignored or their effects are included in complicated ways. For example, their effects may be included through an impedance renormalization process that requires knowledge of all off-state impedances (which are usually obtained with separate calibrations) and typically requires many calibrations at the user plane.
Techniques are needed to reduces the number of calibration steps required (and potential for mistakes) without sacrificing much accuracy.